(I will try to collect reworked versions of my comments to the question to get something like an answer:)
I would suggest to check for the suspicion that the blotches are little graphics once pasted (inadvertently) into the sheet…
Questioning back: Were you able to select such a blotch by a simple LeftClick?
Quoting BladeRunner714: "Yes. That’s when the Formatting toolbar is replaced by the Image toolbar. By the way, I should have mentioned this is on a Mac if that makes a difference.
Lupp again:
(I dont’t know anything about the specifics of OS X. I also never use the ‘Image’ toolbar but …)
There is a ‘Drawing’ toolbar which has a selector tool (big white arrow left, upward) on top by default. Using this “pointing device” with left MouseButton pressed you may draw a selecting frame containing as many graphical objects as you want. By releasing the button you make all the objects inside selected as a volatile group. ‘Del’ should delete them in one go. Please note: Objects get selected only if they are completely inside the frame. This restriction also applies to parts of the images being factually invisible. Don’t be stingy with your frame.
(Acknowledged as solution.)